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The Wave-functionCollapse: Fallacy or Fraud

Sagar Kapadia

Published Aug 21, 2026• 0 citations
Publisher

Abstract

This paper argues that the wavefunction collapse is neither a physical reality nor a fundamental law of nature, but an artificial mathematical patch necessitated by the importation of continuous differential manifolds into a natively discrete domain. By tracing the historical divergence between Werner Heisenberg's discrete matrix mechanics and John von Neumann's axiomatic projection postulate, the study exposes the measurement crisis as a procedural artifact rather than a deep metaphysical mystery. The work demonstrates that matrix mechanics, operating on discrete transition indices, requires no collapse mechanism because it never introduces continuous spreading waves in the first place.

DOI
10.5281/zenodo.22041814

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This paper argues that the wavefunction collapse is neither a physical reality nor a fundamental law of nature, but an artificial mathematical patch necessitated by the importation of continuous differential manifolds into a natively discrete domain. By tracing the historical divergence between Werner Heisenberg's discrete matrix mechanics and John von Neumann's axiomatic projection postulate, the study exposes the measurement crisis as a procedural artifact rather than a deep metaphysical mystery. The work demonstrates that matrix mechanics, operating on discrete transition indices, requires no collapse mechanism because it never introduces continuous spreading waves in the first place.
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This paper presents a formal mathematical and epistemological refutation of canonical and path-integral field quantization protocols. The work demonstrates that forcing discrete quantum operators onto a continuous manifold (R4\mathbb{R}^4R4) constitutes a profound category error—an Aristotelian logical refutation showing that the Planck scale is merely the forced discretization of an artificial continuous cosmos. Furthermore, it exposes the foundational impedance mismatch between Schrödinger’s continuous Wave Mechanics and Heisenberg’s native discrete Matrix Mechanics, proving that infinite potentials, ultraviolet divergences, and renormalization schemes serve as unfalsifiable pseudo-scientific hypotheses designed to rescue broken differential equations from collapse.
This paper argues that unitary time evolution — the continuous, deterministic, reversible evolution of the wave function via the Schrodinger equation — is not a fundamental feature of quantum reality but a continuous approximation of an underlying discrete process, structurally parallel to how Newtonian mechanics approximates discrete molecular dynamics. The measurement problem is identified not as a feature of quantum reality but as an artifact of imposing continuous formalism on discrete physics. A continuous equation cannot produce discrete events; this is mathematical, not mysterious. Caldirola's finite-difference quantum mechanics is cited as the formal precedent. Companion paper to DOI: 10.5281/zenodo.19540088.
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. We compare the theory to the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle, and argue that the new theory lends itself well to a realist interpretation of the wavefunction.
This work proposes that the discreteness observed in quantum mechanics is not a property of objective reality but an artifact of humanly bounded measurement frameworks. By distinguishing between the Ontic State — what exists — and the Epistemic Observation — what can be measured — the framework demonstrates that the continuous deterministic evolution of the Schrödinger equation represents the true underlying reality, while discrete eigenvalues emerge only through the spectral decomposition of measurement operators. The work further argues that quantum jumps are continuous transitions bounded by the decoherence timescale of the measuring apparatus, that quantum randomness is a dimensional projection loss rather than fundamental chaos, and that the contradiction between General Relativity and Quantum Mechanics is a measurement framework artifact rather than a property of nature. A testable prediction is proposed — that finite continuous transition time during quantum state changes is detectable in principle through attosecond spectroscopy.
The quantum measurement problem — the question of what physically occurs when a quantum system yields a definite outcome upon measurement — has remained unresolved since von Neumann's formalization of quantum mechanics in 1932. Existing interpretational frameworks each address aspects of this problem while leaving a specific mechanistic gap unfilled. The Copenhagen interpretation declares collapse without explaining it. The many-worlds interpretation removes collapse but cannot specify the preferred measurement basis. Pilot wave theory identifies a guiding field without identifying what it is. Relational quantum mechanics correctly describes the relational structure of measurement outcomes without specifying the physical process by which relational facts are established. Decoherence theory specifies which outcomes are available through environmental selection without explaining which outcome actually occurs. In each case the effect of measurement is described with precision while the mechanism remains absent. This paper proposes that the Dimensional Evolution geometric framework provides that mechanism. Wavefunction collapse is resonant selection — the stabilization of a specific harmonic configuration when an observer's resonance structure synchronizes with a quantum system's scan traversal through a completed entropic pathway. This is not a metaphysical claim. It is a physically grounded geometric process from which the measurement postulates of standard quantum mechanics emerge as derived consequences rather than foundational axioms. The Born rule reflects the fractal exponential geometry of the coherence manifold. The preferred basis is geometrically specified by observer-system resonance compatibility. The measurement cut dissolves into a continuous spectrum of resonance stability requiring no quantum-classical boundary. The definite outcome problem is resolved by resonant synchronization completing — a deterministic geometric event whose apparent randomness reflects incomplete knowledge of resonance conditions rather than fundamental indeterminacy. The paper maps DE's resonant selection mechanism against each major interpretation, identifying precisely where DE does explanatory work each interpretation cannot. Three testable experimental predictions are proposed — geometry-dependent collapse timing, resonance-bandwidth-dependent outcome distributions, and a geometric memory effect in measurement apparatus — each grounded in physical principles confirmed at other scales and each distinguishable from standard quantum mechanical and decoherence predictions. The implications of this account for the Heisenberg uncertainty relation are identified as a priority for subsequent formal development.